Problem: Simplify the following expression: $ n = \dfrac{-8k - 4}{6k} - \dfrac{-4}{5} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-8k - 4}{6k} \times \dfrac{5}{5} = \dfrac{-40k - 20}{30k} $ Multiply the second expression by $\dfrac{6k}{6k}$ $ \dfrac{-4}{5} \times \dfrac{6k}{6k} = \dfrac{-24k}{30k} $ Therefore $ n = \dfrac{-40k - 20}{30k} - \dfrac{-24k}{30k} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-40k - 20 + 24k }{30k} $ Distribute the negative sign: $n = \dfrac{-40k - 20 + 24k}{30k}$ $n = \dfrac{-16k - 20}{30k}$ Simplify the expression by dividing the numerator and denominator by 2: $n = \dfrac{-8k - 10}{15k}$